# Lower Bounds of Optimal Exponentials of Thickness in Geometry Rigidity Inequality for Shells

## TL;DR

This paper establishes lower bounds for the exponential factors related to the geometry rigidity inequality in shells, revealing how these bounds depend on the shell's curvature type.

## Contribution

It provides the first explicit lower bounds for the optimal exponentials in the geometry rigidity inequality for different shell geometries.

## Key findings

- Lower bound of 4/3 for hyperbolic shells
- Lower bound of 3/2 for parabolic shells
- Lower bound of 1 for elliptic shells

## Abstract

The optimal exponentials of the thickness in the geometry rigidity inequality of shells represent the geometry rigidity of the shells. We obtain that the lower bounds of the optimal exponentials are $4/3,$ $3/2,$ and $1,$ for the hyperbolic shell, the parabolic shell, and the elliptic shell, respectively, through the construction of the Ans\"{a}tze.